论文标题
具有$δ$相互作用的二次通道中的Kronig-Penney模型。 II：散射方法
The Kronig-Penney model in a quadratic channel with $δ$ interactions. II : Scattering approach
论文作者
论文摘要
本文的主要目的是在具有$δ$相互作用的二次通道中引入散射方法，以研究Kronig-Penney模型的研究，该方法在本系列的第一篇论文中以一般性进行了讨论。特别是，一个世俗方程将根据单个$δ$从散射矩阵来编写频谱的世俗方程。这种方法将在[0，\ frac {1} {2}）$中以总能量$ e \在解决域而得到证明，即，在关键交互强度下，对于单个$δ$情况，已知离散频谱已知。将其扩展到对周期案例的研究表明，浮雕光谱和相应的光谱带的行为非常令人惊讶。这些频段的计算可以通过数值进行，并且主要特征可以根据为此目的开发的半古典框架来定性解释。
The main purpose of the present paper is to introduce a scattering approach to the study of the Kronig-Penney model in a quadratic channel with $δ$ interactions, which was discussed in full generality in the first paper of the present series. In particular, a secular equation whose zeros determine the spectrum will be written in terms of the scattering matrix from a single $δ$. The advantages of this approach will be demonstrated in addressing the domain with total energy $E\in [0,\frac{1}{2})$, namely, the energy interval where, for under critical interaction strength, a discrete spectrum is known to exist for the single $δ$ case. Extending this to the study of the periodic case reveals quite surprising behavior of the Floquet spectra and the corresponding spectral bands. The computation of these bands can be carried out numerically, and the main features can be qualitatively explained in terms of a semi-classical framework which is developed for the purpose.
